Experimental & Behavioral Economics · decisions Top choice misrep. % of misrep. MD 261 49 18.8% 167 47 28.1% PD 106 6 5.7% 63 6 9.5% MPD 113 10 8.8% 74 9 12.1% Total 480 65 13.5%

Experimental & Behavioral Economics

Lecture 12: Matching experiments.

Rustamdjan Hakimov, Dorothea Kübler Summer term 2016

Matching • Matching is a subfield of market design

• Markets without money

• In matching problems an agent is paired with an indivisible good (or another agent), and the allocation depends not only on the preferences of the former but also on preferences or a selection criterion form the latter.

• Examples: medical labor market, school choice, college admissions, kidney exchange, lawyers assignments to courts, appointments allocation…

Matching problems

• Matching problems: two-sided and one-sided

• Two-sided problem: marriage market (NRMP, University admissions like in US…)

• One-sided problem: agents have preferences and can be strategic, while objects have priorities and are not strategic (School choice)

School choice • History in US. Everyone has to go to own

district school – Local tax –based financing

– Huge quality differences

– Socio-economic segregation, including racial

• Starting from late 70s: School choice – Parents submit list of their preferences to an

authority

– Based of priorities of the schools allocation of students is done (Sibling, walking zone priorities, otherwise random)

Boston mechanism (BOS)

• All applications are sent to the first choice of students

• If there are more applicants than schools’ capacity, student's of the lowest priority are rejected. Those who are not rejected are ASSIGNED to a corresponding school.

• Quotas of schools are updated.

• Example:

Priorities of schools

A B C

i_1 i_2 i_3 i_2 i_3 i_2

i_3 i_1 i_1

Preferences of students

i_1 i_2 i_3

B A B

A C A C B C

Boston Step 1 A B C i_2 i_1

i_3

Final assignments

A B C i_2 i_3





• Example:


A B C

i_1 i_2 i_3 i_2 i_3 i_2

i_3 i_1 i_1


i_1 i_2 i_3

B A B

A C A C B C

Boston Step 2 A B C i_1

Final assignments

A B C i_2 i_3





• Example:


A B C

i_1 i_2 i_3 i_2 i_3 i_2

i_3 i_1 i_1


i_1 i_2 i_3

B A B

A C A C B C

Boston Step 3 A B C i_1

Final assignments

A B C i_2 i_3 i_1

Deferred acceptance mechanism (DA or GS)


• If there are more applicants than schools’ capacity, student's of the lowest priority are rejected. Those who are not rejected are TENTATIVELY assigned to a corresponding school.

• Applications of rejected students are sent and considered TOGETHER with tentatively accepted students.

• Example:


A B C

i_1 i_2 i_3 i_2 i_3 i_2

i_3 i_1 i_1


i_1 i_2 i_3

B A B

A C A C B C

DA Step 1 A B C i_2 i_1

i_3

Tentative assignments

A B C i_2 i_3





• Example:


A B C

i_1 i_2 i_3 i_2 i_3 i_2

i_3 i_1 i_1


i_1 i_2 i_3

B A B

A C A C B C

DA Step 2 A B C i_2 i_3 i_1

Tentative assignments

A B C i_1 i_3





• Example:


A B C

i_1 i_2 i_3 i_2 i_3 i_2

i_3 i_1 i_1


i_1 i_2 i_3

B A B

A C A C B C

DA Step 2 A B C i_1 i_3 i_2

Final assignments

A B C i_1 i_3 i_2

Top Trading Cycles mechanism (TTC)

• All students at the top of priority of a school “own” all seats of the school

• Every student point to a student who owns her favorite school

• There is at least one cycle, trades are implemented, quotas are adjusted and new “owners” are assigned.

• Example:

• TTC step 1.


A B C

i_1 i_2 i_3 i_2 i_3 i_2

i_3 i_1 i_1


i_1 i_2 i_3

B A B

A C A C B C

Final assignments

A B C i_2 i_1

(i_1, A) (i_2, B)

(i_3, C)

Top Trading Cycles mechanism (TTC)

• All students at the top of priority of a school “own” all seats of the school

• Every student point to a student who owns her favorite school

• There is at least one cycle, trades are implemented, quotas are adjusted and new “owners” are assigned.

• Example:

• TTC step 2.


A B C

i_1 i_2 i_3 i_2 i_3 i_2

i_3 i_1 i_1


i_1 i_2 i_3

B A B

A C A C B C

Final assignments

A B C i_2 i_1 i_3

(i_3, C)

Summary of predictions of mechanism

BOS DA TTC

Strategy-proof No Yes Yes

Stable (no justified envy) No Yes No

Pareto efficient Yes No Yes

Chen and Sönmez (2006) • Compare DA, TTC and BOS in the setup of school

choice

• One-shot

• Information: only induced preferences and district school. No information about preferences. Random priorities in non-district schools

• Two markets: designed and random, but adjustment for trivial decision

• 36 students, 7 schools, total number of seats equals 36

Results. Chen and Sönmez (2006)

Truth-telling in BOS is lower than in TTC and DA. However, the truth-telling rates in DA and TCC are far from universal

Results. Efficiency. Chen and Sönmez (2006)

Designed GS>TTC>BOS Random BOS>GS>TTC

Information in school choice. Pais and Pinter (2008)

• Compare DA, TTC and BOS in the setup of school choice under different information

• 5 teachers, 3 schools with 5 positions

• 4 informational treatments: – Zero information (only own preferences)

– Low information (Chen and Sönmez, 2006)

– Partial information (priorities of other students)

– Full information (full preference and priorities profiles)

Results. Pais and Pinter (2008)

How do we help people to report truthfully? Guillen and Hing (2013)

• Advice in TTC

• Individual decision making setup –playing against computer

• 4 schools, one seat each, 4 students

• Third party (newspaper or forum) advice by 4 treatments: – Baseline (no advice)

– Right advice: The mechanism is designed so that truthful reporting maximizes your chances of getting favored schools.

– Wrong advice: Since the top schools will have many applicants you should be realistic and apply to schools where you are likely to gain acceptance.

– Both

Results. Guillen and Hing (2013)

Is there demand effect?

Field experiment. Guillen and Hakimov (2016)

• Topic allocation problem (School choice problem) (smartphone, TV set and Scanner)

• Top Trading Cycles mechanism: strategy-proof

• Treatments:

1. Detailed mechanism description (MD)

2. Property description and advice (PD)

3. Both (MPD)

Results. Guillen and Hakimov (2016)

Treatment Sample

size

Top choice

misrep. % of misrep.

Non-

trivial

decisions

Top

choice

misrep.

% of misrep.

MD 261 49 18.8% 167 47 28.1%

PD 106 6 5.7% 63 6 9.5%

MPD 113 10 8.8% 74 9 12.1%

Total 480 65 13.5% 304 62 20.3%

Misrepresentation rates by treatments

Strong positive effect of advice. In line with Braun et al. (2014)

Results. Guillen and Hakimov (2016)

Tentative topic

N

Number of misrepresentation

s of the top choice

Number of students

affected by TTB

Proportion of truth

MD TV set 93 31 30 66.67%

PD TV set 40 3 3 92.50%

MPD TV set 40 9 8 77.50%

How do we help people to report truthfully? Ding and Schotter (2016a)

• 4 types of subjects (preferences)

• 3 types of objects

• Type 1 priority in A


• Type 3 priority in B

• BOS16, BOS10, GS16

• Some subject can chat for 5 minutes between Phase 1 and Phase 2.

How do we help people to report truthfully? Ding and Schotter (2016a)

• Strategy changes (Effect of chatting)

Intergenerational advice and learning in DA. Ding and Schotter (2016b)

• 4 types of subjects (preferences)

• 3 types of objects



• Type 3 priority in B

• BOS, GS

• Repeated play versus intergenerational advice

Intergenerational advice and learning in DA

Documents

Experimental & Behavioral Economics · decisions Top choice misrep. % of misrep. MD 261 49 18.8% 167 47 28.1% PD 106 6 5.7% 63 6 9.5% MPD 113 10 8.8% 74 9 12.1% Total 480 65 13.5%